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a screen is placed 90cm from an object. the image of an object on the screen is formed by a convex lens at two different locations separated by 20cm. the focal length of the lens is?

a screen is placed 90cm from an object. the image of an object on the screen is formed by a convex lens at two different locations separated by 20cm. the focal length of the lens is?

Grade:12

6 Answers

kamakshi
24 Points
8 years ago
If the object has two images then the object is placed at the focus and the emergent rays are parallel to the principal axis. Imagine a point object in front of a convex lens.Now two light rays emerge from the object each one is refracted in such a way that they become parallel to the principal axis.Now these two rays hit the screen and appear as two different images. thus it is safe to say that the focal length is equal to the object distance i.e. 90 cm. Please verify this answer. I hope this was at least a little helpful.
vaanya
18 Points
8 years ago
no, the answer is 21.4 cm. i dunno how to do it but i think its got sumthn to do with the u-v method of finding focal length in which the lens is shifted to get two distinct images, one diminished and one enlarged. but still thanks for trying to help :)
abishek
19 Points
5 years ago
1/f=1/v-1/u at position 1
1/f=(1/v-20)-(1/u+20)
1/v-1/u=(1/v-20)-(1/u+20)
solve it and get the answer
answer is 21.4cm
Oindrila Ghosh
49 Points
5 years ago
use the formula, f=D^2-d^2/4D,where D=100cm and d= 20cm.
Now,by putting the values of d and D in the above formula ,calculate the focal length.
B Balakrishna
11 Points
4 years ago
Distance from object to screen is 90u+v=90; difference in location of lens is 20So u-v=20......by solving we get u= 35 or 55 and v=55 or 35Then by using lens formula f=21.38 cm
Rishi Sharma
askIITians Faculty 646 Points
2 years ago
Dear Student,
Please find below the solution to your problem.

If the object has two images then the object is placed at the focus and the emergent rays are parallel to the principal axis. Imagine a point object in front of a convex lens.Now two light rays emerge from the object each one is refracted in such a way that they become parallel to the principal axis.Now these two rays hit the screen and appear as two different images. thus it is safe to say that the focal length is equal to the object distance i.e. 90 cm

Thanks and Regards

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